Being a Muslim, it Is our faith that God has all abilities to do anything, so is it possible for God to create so heavy rock that he can not lift himself?
Before answering your question, I would like to clarify what the concept of 'omnipotence'1, as used with reference to God, implies. To fully understand the implication of the 'omnipotence' of God, we should keep in mind that God is not ONLY 'omnipotent'. God's omnipotence is subject to His mercy, wisdom, omniscience and His other attributes. Therefore, it would not be very accurate to say that 'God can do everything/anything'. A more accurate statement would be 'God can do everything/anything that His wisdom/mercy/omniscience/etc. require Him to do'. Hence, even though God is 'omnipotent', yet He CANNOT do anything, which is contrary to His other attributes. Thus, one may ask: "If God is 'omnipotent', can He create another one like Himself?" Or "if God is 'omnipotent' can He commit suicide?" Or "If God is 'omnipotent', can he throw the pious in Hell and place the evil in heaven?" All these questions are, in fact, based on a 'Playing Tom' view of an omnipotent God. God is absolutely clear of all wrong and, therefore, even though He is 'omnipotent', yet He CANNOT do anything, which is against His wisdom, justice, knowledge etc. It should, therefore, remain clear that God's omnipotence is conditional upon His other attributes.
Keeping the foregoing clarification in perspective, let us now turn to your specific question.
The fact that God is 'omnipotent' implies that, if His wisdom so requires, there is no limit on the largeness of a stone that He can make. It also implies that, if His wisdom so requires, there is no limit on His capacity of lifting stones. Both the capacities – that of creation as well as that of lifting – are unlimited; neither of the two knows any limits. Now, when someone asks whether God can make a stone, which He Himself cannot lift, the question can actually be rephrased as: 'Can God limit His power of creation?' or 'Can God limit His power of lifting stones?'. In other words, the question, in fact, is similar to 'Can God create something (a stone), upon which He loses control?' or that 'Can God create another God?'.
The answer to all these questions is 'No, God cannot do anything, which is contrary to His wisdom and His other attributes'.
I hope this helps.
1. i.e. the ability to do everything or the concept that nothing is impossible for God.